EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 134: step-by-step solution

Step through the whole solution, or skip to the hard parts. Blue digits are placed by the walkthrough; red strike-through marks a candidate being ruled out.

Puzzle
Sudoku, number 134 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
24 of 46 steps need an advanced or expert technique

Blue digits are placed by the walkthrough. Red strike-through marks a candidate being ruled out. Cells are named by row and column: R3C5 is row 3, column 5. Arrow keys step too.

The key technique: XY-Chain

A chain of two-candidate cells, each linked to the next. Whichever way the start cell goes, one end of the chain holds the digit, so cells seeing both ends cannot.

Other advanced and expert techniques in this solve: ALS-XZ (×3), Finned Fish (×3), Nice Loops/AICs (×3), Empty Rectangle (×2), XY-Wing (×2), 2-String Kite, Cell Forcing Chains, Coloring/Multi-coloring, Skyscraper, WXYZ-Wing, X-Wing/Swordfish.

Every move above the basics is listed on the sudoku techniques page, each with a one-sentence explanation and worked examples from the books.

The hard steps, in text (24)
  1. Step 4 · 2-String Kite advanced
    Rules out 7 from R7C2.
  2. Step 5 · Finned Fish expert
    Rules out 8 from R7C8.
  3. Step 6 · ALS-XZ expert
    Rules out 3 from R5C9.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 1 from R1C9.
  5. Step 8 · Cell Forcing Chains expert
    Rules out 3 from R1C1; 7 from R1C1.
  6. Step 11 · Skyscraper advanced
    Rules out 7 from R5C5.
  7. Step 13 · Finned Fish expert
    Rules out 7 from R1C7.
  8. Step 14 · WXYZ-Wing expert
    Rules out 3 from R2C8, R2C9.
  9. Step 15 · Empty Rectangle advanced
    Rules out 3 from R4C7.
  10. Step 16 · Empty Rectangle advanced
    Rules out 3 from R7C7.
  11. Step 17 · ALS-XZ expert
    Rules out 2 from R5C9.
  12. Step 18 · Nice Loops/AICs expert
    Rules out 3 from R1C7.
  13. Step 19 · ALS-XZ expert
    Rules out 5 from R2C9.
  14. Step 21 · Nice Loops/AICs expert
    Rules out 7 from R5C3, R7C3, R9C3.
  15. Step 22 · Coloring/Multi-coloring expert
    Rules out 7 from R7C1.
  16. Step 26 · XY-Chain expert
    Rules out 3 from R1C9.
  17. Step 29 · X-Wing/Swordfish advanced
    Rules out 7 from R7C7, R9C7.
  18. Step 31 · Finned Fish expert
    Rules out 2 from R4C4.
  19. Step 32 · XY-Chain expert
    Rules out 3 from R1C8.
  20. Step 36 · XY-Chain expert
    Rules out 5 from R4C5.
  21. Step 37 · XY-Chain expert
    Rules out 5 from R4C4, R5C8, R5C9.
  22. Step 39 · XY-Wing advanced
    Rules out 4 from R7C8, R9C5.
  23. Step 40 · XY-Chain expert
    Rules out 5 from R9C7.
  24. Step 41 · XY-Wing advanced
    Rules out 8 from R9C3.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, ramping from hard to brutal.

150 new puzzles. Expert and beyond. Puzzles by M. J. Bailey. Paperback, 5 × 8 in, 196 pages, £9.99 / $11.99. Every solution in the book carries a QR code to its own walkthrough, so you can check one step without seeing the whole answer.

On Amazon from 8 Dec About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Killer Sudoku 3.